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Improving MCMC, using efficient importance sampling

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  • Liesenfeld, Roman
  • Richard, Jean-François

Abstract

A generic Markov Chain Monte Carlo (MCMC) framework, based upon Efficient Importance Sampling (EIS) is developed, which can be used for the analysis of a wide range of econometric models involving integrals without analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components, such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC-EIS approach is illustrated with simple univariate integration problems, and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes.

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  • Liesenfeld, Roman & Richard, Jean-François, 2008. "Improving MCMC, using efficient importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 272-288, December.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:272-288
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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    3. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    4. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    5. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    6. Luc Bauwens & Nikolaus Hautsch, 2006. "Stochastic Conditional Intensity Processes," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 450-493.
    7. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    9. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
    10. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    11. Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford.
    12. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    13. RICHARD, Jean-François, 1977. "Bayesian analysis of the regression model when the disturbances are generated by an autoregressive process," LIDAM Reprints CORE 317, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Patrick Sevestre & Laszlo Matyas, 2008. "The Econometrics of Panel Data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00279977, HAL.
    15. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    16. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
    17. Steven Stern, 1997. "Simulation-Based Estimation," Journal of Economic Literature, American Economic Association, vol. 35(4), pages 2006-2039, December.
    18. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    19. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Estimation of Dynamic Bivariate Mixture Models: Comments on Watanabe (2000)," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 570-576, October.
    20. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    21. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1, July-Dece.
    22. BAUWENS, Luc & HAUTSCH, Nikolaus, 2003. "Dynamic latent factor models for intensity processes," LIDAM Discussion Papers CORE 2003103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    23. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    24. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
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    Cited by:

    1. Bastian Gribisch, 2016. "Multivariate Wishart stochastic volatility and changes in regime," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 443-473, October.
    2. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
    3. Naylor, J.C. & Tremayne, A.R. & Marriott, J.M., 2010. "Exploratory data analysis and model criticism with posterior plots," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2707-2720, November.
    4. Bauwens, L. & Galli, F., 2009. "Efficient importance sampling for ML estimation of SCD models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1974-1992, April.
    5. Raices Cruz, Ivette & Lindström, Johan & Troffaes, Matthias C.M. & Sahlin, Ullrika, 2022. "Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    6. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.

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